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OCEANO-50; No. of Pages 14

Oceanologia (2016) xxx, xxx—xxx

Available online at www.sciencedirect.com

ScienceDirect

j ournal homepage: www.elsevier.com/locate/oceano

ORIGINAL RESEARCH ARTICLE

Modeling the buoyancy-driven Black Water

outflow into the North

Nikolaos Kokkos, Georgios Sylaios *

Department of Environmental Engineering, Democritus University of , ,

Received 30 July 2015; accepted 29 December 2015

KEYWORDS Summary A three-dimensional numerical model was applied to simulate the Water

(BSW) outflux and spreading over the North Aegean Sea, and its impact on circulation and

Hydrodynamic model;

stratification—mixing dynamics. Model results were validated against satellite-derived sea

Remote sensing data;

surface temperature and in-situ temperature and salinity profiles. Further, the model results

Model validation;

were post-processed in terms of the potential energy anomaly, f, analyzing the factors contrib-

Potential energy

anomaly; uting to its change. It occurs that BSW contributes significantly on the Thracian Sea water column

stratification, but its signal reduces in the rest of the North Aegean Sea. The BSW buoyancy flux

North Aegean Sea

3 3

contributed to the change of f in the Thracian Sea by 1.23 10 W m in the winter and

4 3

7.9 10 W m in the summer, significantly higher than the corresponding solar heat flux

5 3 5 3

contribution (1.41 10 W m and 7.4 10 W m , respectively). Quantification of the f-

advective term crossing the north-western BSW branch (to the north of Island), depicted a

strong non-linear relation to the relative vorticity of Samothraki Anticyclone. Similar analysis for

the south-western branch illustrated a relationship between the f-advective term sign and the

relative vorticity in the system. The f-mixing term increases its significance under

1

strong winds (>15 m s ), tending to destroy surface meso-scale eddies.

# 2016 Institute of Oceanology of the Polish Academy of Sciences. Production and hosting by

Elsevier Sp. z o.o. This is an open access article under the CC BY-NC-ND license (http://

creativecommons.org/licenses/by-nc-nd/4.0/).

* Corresponding author at: Vas. Sofias 12, 67100 Xanthi, Greece. Tel.: +30 25410 79398; fax: +30 25410 79398.

E-mail address: [email protected] (G. Sylaios).

Peer review under the responsibility of Institute of Oceanology of the Polish Academy of Sciences.

http://dx.doi.org/10.1016/j.oceano.2015.12.003

0078-3234/# 2016 Institute of Oceanology of the Polish Academy of Sciences. Production and hosting by Elsevier Sp. z o.o. This is an open

access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

Please cite this article in press as: Kokkos, N., Sylaios, G., Modeling the buoyancy-driven Black Sea Water outflow into the North Aegean Sea.

Oceanologia (2015), http://dx.doi.org/10.1016/j.oceano.2015.12.003

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OCEANO-50; No. of Pages 14

2 N. Kokkos, G. Sylaios

affected strongly by seasonal meteorology (Sylaios, 2011),

1. Introduction

a semi-permanent anticyclone of variable strength and

dimensions developed in the Thracian Sea, around Samo-

The North Aegean Sea (NAS) (Fig. 1) acts as a dilution basin,

thraki and possibly Imvros Islands (Cordero, 1999; Theocharis

directly affected by the buoyancy outflow of the low-salinity,

and Georgopoulos, 1993; Zervakis and Georgopoulos, 2002)

nutrient-rich Black Sea Water (BSW) exported through the

and a rapidly changing cyclone—anticyclone system, covering

Dardanelles Strait, at the north-eastern part of the basin

the upper 200 m of the Sporades Basin. This latter system

(Androulidakis and Kourafalou, 2011). Along the ,

appears supplied either by the higher salinity waters moving

a strongly-stratified two-layer system with opposing flows is

from the southern Aegean Sea or by the fresher water of BSW

formed, consisting of the exiting to the NAS surface BSW layer

(Kontoyiannis et al., 2003). Other eddy features of variable

and the outflowing into the bottom layer

strength and size appear dependent on BSW discharge and

(Ünlüata et al., 1990). The significant vertical shear stresses

Thermaikos Gulf freshwater outflows (Olson et al., 2007).

developed at the system's interface favor the upward entrain-

Several previous modeling efforts exist, using mostly the

ment, thus returning parts of NAS water back to the Aegean

Princeton Model (POM), applied under variable spatial

(Karnaska and Maderich, 2008). Recent estimates of the annual

3 1 resolution grids and different boundary conditions for the

BSW discharge report values ranging between 38,820 m s

3 1 BSW outflux. Zodiatis et al. (1996) used a two-dimensional

(Karnaska and Maderich, 2008) and 42,790 m s (Tuğrul

vertically-integrated model to simulate the synoptic-scale

et al., 2002), with approximately 67% of its volume being

flow patterns of the NAS and utilized NOAA-AVHRR thermal

directly transferred from the Marmara Sea and 33% attributed

images for model validation. Korres et al. (2002) coupled a

to NAS water entrainment. After its outflow, BSW occupies the

high resolution atmospheric model with POM and assessed

first 50 m of the water column, overlying on the northward

model's skill in forecasting the satellite-recorded sea surface

flowing warm and highly saline Levantine Intermediate Water

temperature (SST) field. Kourafalou and Barbopoulos (2003)

(LIW), between a depth of 50 m and 400 m, and the North

used the modified sigma-coordinated POM in a high resolution

Aegean Deep Water (NADW) from 400 m to the bottom

mode (2.5 km 2.5 km), nested at its southern boundary to a

(Zervakis et al., 2000). Its impact on surface dynamics of

coarse grid Mediterranean model and a regional, intermediate

NAS exhibits strong seasonality, especially during early spring,

resolution model. BSW discharge boundary condition was

when the mean monthly outflux through the Dardanelles

3 3 1 determined by the net monthly inflow-outflow budget at

Straits reaches 450 km per season (57,740 m s ), as a result 3 1

the Dardanelles, ranging from 5000 m s in December to

of the increased river runoff and precipitation over the Black 3 1

15,000 m s in June. Kourafalou and Tsiaras (2007) applied

Sea and the raised local entrainment fluxes at the Dardanelles

POM in a 1.6 km 1.6 km grid imposing a two-layer (inflow-

(Tuğrul et al., 2002).

outflow) transport rate at the Dardanelles boundary. Tzali

The exit of BSW from the Dardanelles produces a cyclonic

et al. (2010) applied POM in a series of BSW outflow scenarios,

flow, bifurcating at Lemnos Island, with the southern branch

to assess the impact of BSW inflow rate on the established NAS

being stronger during the summer, under the influence of the

circulation. Finally, Androulidakis and Kourafalou (2011)

annual northerly Etesian winds, and the northern branch

applied the Hybrid Coordinate Ocean Model (HYCOM) on a

covering the entire Thracian Sea continental shelf (Vlasenko

very high resolution grid (1/508 1/508) and introduced a new

et al., 1996; Zervakis and Georgopoulos, 2002). In winter BSW

mathematical scheme for BSW outflow rates. Model validation

core concentrates at the northern coast of Lemnos Island,

involved the comparison of model results to satellite and in situ

where it bifurcates primarily to the north-west and occa-

data.

sionally to the southwest, under the influence of north-east-

The present paper presents the results of a three-dimen-

erly (bora-type) gales. The most prominent surface patterns

sional hydrodynamic model for the thermohaline NAS circu-

in NAS include the thermohaline BSW-LIW frontal zone,

lation, placing particular emphasis on (a) the model

validation procedure, by comparing surface model results

with extensive satellite datasets and CTD profiles from field

campaigns, (b) the stratification—mixing conditions of BSW

along its route over NAS, (c) the quantification of individual

terms of the potential energy anomaly general equation, and

(d) the description of the permanent and semi-permanent

surface meso-scale patterns, developed in NAS and their

inter-link to BSW buoyancy spreading.

2. Material and methods

2.1. Model description

The hydrodynamic Estuary and Lake Computer Model

(ELCOM), a three-dimensional numerical model developed

by the Centre for Water Research at the University of Western

Australia (Hodges and Dallimore, 2001) was used for modeling

the NAS. This model has mostly been used to simulate the

Figure 1 The North Aegean Sea and its physiographic basins. hydrodynamics of lakes and reservoirs, but it has also been

Please cite this article in press as: Kokkos, N., Sylaios, G., Modeling the buoyancy-driven Black Sea Water outflow into the North Aegean Sea.

Oceanologia (2015), http://dx.doi.org/10.1016/j.oceano.2015.12.003

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OCEANO-50; No. of Pages 14

Modeling the buoyancy-driven Black Sea Water outflow into the North Aegean Sea 3

applied in the modeling of buoyancy fluxes and geophysical the bottom. All variables were located at fixed z-levels

flows at large-scale enclosed basins, estuaries and coastal (z-coordinate model), thus producing a computational

, as the (Alosairi et al., 2011), the Northern domain comprised by 3,109,280 rectangular finite-volumes.

Adriatic Sea (Spillman et al., 2007) and the (Barry

et al., 2009). Kopasakis et al. (2012) modeled successfully NAS 2.2.2. Initial and boundary conditions

water circulation and pollutants accumulation, while Kamidis A constant initial condition over the grid domain (T = 108C

et al. (2011) validated the model to simulate the transport and and S = 38.0 psu) was determined for the ambient water of

diffusion processes in River plume. Further, Sylaios NAS. Model boundary conditions involved hydrologic,

et al. (2013) utilized the above model-validated results to meteorological and tidal forcing. Hydrologic forcing was

fi

assess the along- and cross-shore circulation and the strati - determined on a mean monthly basis by applying river dis-

fi

cation-destrati cation processes in the shallow and elongated charge and water temperature for all main rivers of Greece

Thassos Passage (Thracian Sea). and , as reported by Skoulikidis et al. (1998). BSW

ELCOM solves the Reynolds-Averaged Navier Stokes equa- buoyancy flux was considered seasonally variable, with a

3 1 3 1

tions, using both the hydrostatic and the Boussinesq approx- mean annual value of 42,222 m s or 1331 km yr , as

imations. The numerical method applies a semi-implicit computed by Tuğrul et al. (2002). BSW daily temperature

fi

formulation on a nite-volume framework using rectangular was extracted from MODIS SST satellite data for the Sea of

Cartesian cells in an Arakawa-C grid stencil (Hodges, 2000). Marmara. BSW salinity at the Dardanelles boundary varied

fi

Horizontal grid spacing is xed, whereas the vertical spacing seasonally, with a mean annual value of 28.03 psu, following

may vary as a function of depth, but remains horizontally Türkoğlu (2010).

fi

uniform and xed over time. Free-surface evolution in each Meteorological time-series for a four-year period (2005—

grid cell's column is solved by the vertical integration of the 2008) with a 3 hrs time-step were acquired from the NOAA

fl

conservation of mass equation for incompressible ow database (http://ready.arl.noaa.gov/READYamet.php) at

applied to the kinematic boundary condition. 18 18 spatial resolution, to describe the atmosphere-ocean

The numerical scheme follows the adapted TRIM approach boundary conditions. Datasets included wind speed and

fi

(Casulli and Cheng, 1992) with modi cations for scalar con- direction, atmospheric relative humidity, cloud cover, baro-

servation, numerical diffusion, and implementation of a metric pressure, atmospheric temperature, precipitation

mixed-layer turbulence closure (Hodges, 2000). Convective and solar radiation intensity.

—

terms are calculated using a third order Euler Lagrange Boundary temperature, salinity, currents and tidal eleva-

scheme, while the ULTIMATE-QUICKEST scheme is introduced tions at the southern model boundary were obtained from

for the advection of scalars. The model produces the daily MyOcean products (www.myocean.eu) using the Med-

fi

dynamics of strati ed water bodies with external environ- iterranean Sea Physics Re-analysis database (1987—2012).

mental forcing, such as tidal forcing, wind stresses, surface Water temperature, salinity and velocity profiles were

fl fl

thermal forcing as well as in ows and out ows (Hodges and acquired at 72 layers with a daily time-step at a spatial

Dallimore, 2001) and thus seems appropriate for application resolution of 0.06258 along the southern boundary line of

in NAS. Heat exchange through the water's surface is the model's computational grid. Initially, these profiles were

governed by standard bulk transfer models corrected for vertically spline-interpolated to match the layered config-

non-neutral atmospheric stability effects (Imberger and Pat- uration of ELCOM model. At a second stage, a horizontal

terson, 1990). The model does not follow the commonly-used interpolation algorithm, applied to each layer, filled the gaps

eddy diffusivity approach, but adopts a unique 1D mixed- of horizontal model's discretization.

layer model for computing the vertical mixing of momentum The NAS model was run for four consecutive years with a

and scalars (Laval et al., 2003), an approach particularly time-step of 3 min. Year one (2005) was used to develop and

fi

proper for strati ed water bodies as NAS. stabilize the flow field, especially due to BSW entry, while

years 2006—2008 to obtain, compare and post-process model

results. These consisted of the three-dimensional flow field,

2.2. NAS model set-up

the temperature and salinity fields and the sea-surface

height evolution.

2.2.1. Bathymetry and computational domain

Model domain extends from 38.68N to 41.08N and from 22.58E

to 27.08E, thus covering both shelf and deep areas of NAS 2.3. Model validation procedure and criteria

(Fig. 1). The bottom bathymetry was digitized in a Geo-

graphic Information System (MapInfo v10.0), to develop a Model validation was achieved in two manners: (a) by com-

Digital Elevation Model (DEM) from the paring sea-surface temperature model results at 44 regu-

1:200,000 bathymetric chart. Model's computational grid larly-spaced model grid cells with the SST data obtained by

was developed using a spatial mapping tool (Vertical Mapper the International Group for High Resolution SST (GHRSST,

for MapInfo) and the application of linear triangulation inter- www.ghrsst.org), a platform combining daily updates of

polation. The modeled area was discretized into a uniform near-real-time level 2 data (SSTs at observed pixels), level

high resolution horizontal grid consisting of 1 km 1 km 3 data (gridded in space, but with no gap-filling) and level

orthogonal cells (0.0098 0.0098), allowing the accurate 4 data (gap-free objective analysis data), with a

representation of area's complex bathymetry and topogra- 0.258 0.258 spatial resolution (Martin et al., 2012); and

phy. The water column at each horizontal cell was divided (b) by comparing model produced temperature and salinity

into 20 exponentially stretched layers, consisting of thinner profiles with the 2006 CTD casts of summer NAS cruises

surface layers with gradually increasing thickness towards (Sylaios, 2011; Sylaios, unpublished data).

Please cite this article in press as: Kokkos, N., Sylaios, G., Modeling the buoyancy-driven Black Sea Water outflow into the North Aegean Sea.

Oceanologia (2015), http://dx.doi.org/10.1016/j.oceano.2015.12.003

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OCEANO-50; No. of Pages 14

4 N. Kokkos, G. Sylaios

2

To evaluate the validity of model results with satellite and where g is the gravitational acceleration [m s ], z is the

in-situ data, a set of criteria was established (Jedrasik, vertical coordinate pointing upward at the sea surface [m],

3

2005): r is the depth-averaged density [kg m ], r is the local

3

density [kg m ] at depth z, and h is the total water

(a) the correlation coefficient, r, defined as: depth [m]. By definition f is depth independent, but it

varies horizontally and in time. It occurs that f is zero for a

covðoi; miÞ oimio m

¼ ¼ ;

r (1) fully-mixed water column, and positive for stable stratifi- s s s s

o m o m cation.

where oi and mi represent the observed and modeled Although PEA explains the instant state of water column in

fi

paired values (with i = 1, 2, . . ., N), respectively, and o, m terms of mixing and strati cation, the temporal change of

and so and sm the respective means and standard devia- PEA may explain the interacted processes related to mechan-

tions of the observed and modeled datasets. This is the ical mixing (wind and tidal stirring) and stratifying mechan-

fl fl

non-dimensional measure of co-variation of the observed isms as the solar heat ux and the freshwater buoyancy ux

and modeled values, reaching its maximum at unity. Such (Simpson et al., 1991). Therefore, the change of PEA in time

criterion is insensitive to the total model bias. may be expressed as:

fi

(b) the mean squared error, MSE, de ned as:   3 3 " # @f dksr jW j ekbr ju j agQ 1

a w b S ¼ þ þ s 2 ðmoÞ2

2 2 m @t h h 2Cp 320

¼ ð Þ þ þ ; TOTAL

MSE so 1 r r 2 (2) so so 2 4 2 g h @rw

; (6)

N r @x

where the first term is the squared correlation coeffi- Z w

cient; the second term describes the conditional model

where the first term represents the wind stirring influence

bias C, expressing the correlation between model error

and the second term represents the tidal stirring effect, both

and the values simulated by the model; and the third

tending to decrease f over time. d and e are empirically

term the unconditional model bias B, defined as the ratio

determined mixing coefficients (d = 0.039 and e = 0.0038)

of absolute bias to the squared standard deviation of the

expressing the efficiency in the conversion of wind and the

observations. For increased model reliability MSE should

tidally-generated turbulent kinetic energy into potential

be minimum.

energy (Lund-Hansen et al., 1996), ks and kb are the surface

(c) the Nash-Sutcliffe effectiveness coefficient E, defined 5

and bottom drag coefficients (ks = 6.4 10 and

as: 3 3

kb = 2.5 10 ), ra is the air density (1.2 kg m ), rw is

3

MSE the water density [kg m ], h is the water column depth

E ¼ 1 : (3) 1

2 [m] and W and u represent the wind speed [m s ] and so b

1

bottom current velocity [m s ]. The third and fourth terms

It is considered as a dimensionless transformation of

express the stratifying solar heat flux and freshwater buoy-

MSE, also called a quadratic model score. Its value

ancy flux, respectively, tending to increase the f-value in

increases up to unity with increasing model quality.

time. a and Cp are thermal expansion coefficients

4 1 3 1 1

(d) the special correlation coefficient:

(a = 1.6 10 8C at 98C and Cp = 4.0 10 J kg 8C ),

sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2

MSE g is the gravity acceleration [m s ], QS is the incident solar

¼ : 2

Rs 1 (4) heat flux at the sea surface [W m ] and N is the vertical

2 2 Z þ

so m 2 1

eddy viscosity coefficient [m s ], determined as NZ = ghu,

3

where g = 3.3 10 and u the depth-averaged tidal speed

fi A perfect t is reached when Rs = 1, meaning that 1

[m s ].

MSE = 0. Rs better represents the fitting of model simu-

In order to derive the relative impact of each individual

lations to the observed ones, compared to the total

term on the change of the potential energy anomaly of NAS

square error (Jedrasik, 2005), and

water column, the combined Eq. (6) was integrated in time,

(e) the mean modified model bias, defined as the ratio of

for a period of a month, using the mean daily values of

the mean modeled to the mean observed counterpart,

respective parameters, thus:

indicating the over- or under-estimation tendency of the

Z Z simulations. t t

1 3 ag 1

¼ j j þ þ fTOTAL dksra W dt Q S dt

h 0 2Cp 0 320

2.4. Model results post-processing Z Z 2 4 t 2 t

g h @rw 1 3 j j ; dt ekbrw ub dt (7)

NZr @x h

To assess the impact of BSW buoyancy flow path over the w 0 0

near-surface water column (0—200 m depth) of NAS, the

where terms 1 to 4 refer to the relative impact of the wind,

3

potential energy anomaly f (PEA, in J m ) was considered

the incident solar radiation, the BSW buoyancy flux and the

through model results. PEA-values express the stability of the

tide on the total potential energy anomaly of the water

water column, defined as the amount of energy per unit

column. The term (@rw/@x) refers to the model-computed

volume needed to vertically homogenize the water column,

depth-averaged (0—200 m) density gradient between

as (Simpson, 1981):

BSW exit point at the Dardanelles and each selected

Z

studied site throughout NAS. The impact of the tidal term

1 0

f ¼ gzðrrÞ dz; (5) was considered as negligible for the micro-tidal environ-

h h

ment of NAS.

Please cite this article in press as: Kokkos, N., Sylaios, G., Modeling the buoyancy-driven Black Sea Water outflow into the North Aegean Sea.

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OCEANO-50; No. of Pages 14

Modeling the buoyancy-driven Black Sea Water outflow into the North Aegean Sea 5

fi

2.5. Relative contribution of PEA equation terms Term E (vertical mixing) was simpli ed into:

along a meridional transect

@f ju3j

¼ ; CdG r0 (9)

@t Term-E h

To comprehend the impact of advection of BSW pulses on

NAS, the relative magnitude of each term in the general where Cd is the drag coefficient (=0.0025) and G is the mixing

fi

dynamic f-equation was quanti ed, utilizing the ELCOM efficiency coefficient (=0.04).

model results for the upper 130 m layer, corresponding to Terms F and G involving inner sources of density due to

the upper 5 layers, along a meridional transect. The general absorption of solar radiation and the surface and bottom

f-equation derived by Burchard and Hofmeister (2008) buoyancy fluxes appear dominated by surface heating. These

reads: terms could be parameterized according to Wiles et al.

Z Z

0 0 (2006), involving meteorological data (derived from NOAA

@f g ~ g h ~ ~

¼ r ðu Þþ r : u ur

|fflfflfflfflfflffl{zfflfflfflfflfflffl}h f hr z dz h z hrdz database) as the incoming short wave radiation, relative

@t h h h h 2

|fflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflffl} |fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl} A humidity, wind speed and sea albedo for the derivation of

B C

the upward heat flux due to evaporation, the long-wave back

Z Z

0 0

g h ~ r0 r0 s b radiation and the sensible heat transfer, as following: ~ þ ð þ Þ

h z w@zrdz Pb dz Pb Pb h h 2 h h |fflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflffl}2 |fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl} |fflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflffl} @f ag 0

F ¼ ðQ TQ Þ; (10)

D E @t 2C S u

p

Z Z Terms F&G 0 0

g h g h 3 1 1

þ þ r ð r Þ ;

h z Q dz h z h Kh hr dz where Cp is the heat capacity (=4.0 10 J kg 8C ), a is the

h h 2 h h 2 4 1 0

|fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl} |fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl} fi thermal expansion coef cient (=1.51 10 K ), Q S is the

G H

sub-surface incident solar radiation, T is the heat released

(8) when radiation reaches the sea bottom, and Qu is the sum of

~ upward heat flux due to evaporation, long-wave back-radia-

where u and u are the depth-averaged and the deviation from 0

fl

tion and sensible heat ux (Qu = QE + QB + QC). Q S is deter-

the depth-mean horizontal velocity vectors, respectively 0

¼ ð Þ

1 ~ mined by Q S Q S 1 A , where A is the sea surface albedo

[m s ], w is the deviation from depth-mean vertical velocity

1 (=0.15) and QS is the incident solar radiation. T is computed

[m s ], h is the elevation of sea surface above the mean [m],

as a function of the effective diffusive attenuation coeffi-

r and r~ are the depth-averaged and the deviation from the

3 cient for short wave radiation (k = 0.3) and total water depth,

depth-mean densities, respectively [kg m ], r0 is the refer-

3 as:

ence density [kg m ], Q is the source term for density due to

2

heating [W m ], Kh is the horizontal eddy diffusivity 2ð1a1Þ

kh

2 1 T ¼ 1 ð1e Þ; (11)

fl [m s ], Pb is the vertical buoyancy ux (=(g/r0)KZ(@r/ kh

S b

@z)), while Pb and Pb are the surface and bottom buoyancy

2 3 where a1 = 0.55, representing the fraction of heat absorbed

fluxes [m s ], respectively, and 5h is the horizontal gradi-

at the thin surface layer. The upward heat flux terms were

ent operator.

determined using relative humidity and wind velocity data

In the above equation the described processes are:

from NOAA database combined with sea surface temperature

f-advection (term A), representing the advection of

data from the ELCOM model and applying the standard heat

potential energy anomaly by the depth-averaged horizontal

flux formulas (Gill, 1982). All calculations were performed in

velocity vector; the depth-mean straining (term B), repre-

MATLAB 10.

senting the straining of the depth-averaged horizontal den-

sity gradient due to the deviation from the depth-mean

3. Results

velocity vector; the non-mean straining (term C), repre-

senting the straining produced by the deviation from the

depth-averaged horizontal density gradient; the vertical 3.1. Model results validation

advection (term D), produced by the deviation from the

linear vertical velocity proceeding from the kinematic At the first validation stage, daily-averaged SST model results

boundary conditions imposed on the water column surface were compared to satellite recorded SST daily data obtained

and bottom; the vertical mixing (term E), expressed by the from the GHRSST dataset (n = 365 per year). For each station,

fl

integrated vertical buoyancy ux; the surface and bottom the produced scatter points followed closely the diagonal in

fl

density uxes (term F), both increasing f; the heating due the simulated—observed data plots (Fig. 2a and b), providing

to short-wave radiation (term G), representing inner quite successful statistical measures. The spatially-mean

sources or sinks of potential density; and the divergence validation criteria, presented in Table 1, indicate that mod-

fl

of horizontal turbulent density uxes (term H), increasing el's performance improves over time (years 2006—2008).

f at the upper half of the water column. Mean conditional and unconditional model biases of the mean

For our analysis, only terms A, B, C, E, F and G were squared error for all these years were computed at 0.040 and

accounted for as the most important factors controlling the 0.099, respectively. From years 2006 to 2008 the mean

fi —

strati cation mixing dynamics of the area. Following Hoi- modified model bias turns from over- to slight under-estima-

tink et al. (2011), contributions from the temporal and tion of the satellite-derived SST (Table 1). This performance

spatial variations of vertical velocity in the deviation of mean varies spatially and temporally. In the Thracian Sea slight

fi

density (term D) and the impact on strati cation from the winter and autumn over-estimation exists, changing to fair

fl

horizontal divergence of horizontal turbulent density uxes under-estimation in spring and summer (Fig. 2c). Summer

(term H) were considered as negligible. under-estimation appears more prominent in the Sporades

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6 N. Kokkos, G. Sylaios

Figure 2 Scatter diagrams and temporal variability between the modeled and the GHRSST sea-surface temperature data during

2008. Subplots (a) and (c) compare data in the Thracian Sea (circle), and (b) and (d) in the Sporades Basin (diamond).

Basin (Fig. 2d). Such underestimation could also be attrib- At the second validation stage, the model's ability to

uted to the daily-averaging of modeled data, the impact of reproduce the vertical distribution of temperature and sali-

relatively poor meteorological conditions resolution and the nity fields was tested. Year 2006 CTD casts in NAS (103 sam-

fixed horizontal eddy viscosity and diffusivity coefficients. pling sites) were compared to temperature and salinity

Fig. 3 illustrates the spatial variability in the model validation model results, up to 200 m depth. In-situ data were initially

statistical measures for year 2008. Higher correlation coeffi- layer-averaged, to match model discretization, and then

cients were obtained in the Thracian Sea and Thermaikos directly compared to model outputs (n = 457). Validation

Gulf, where the model slightly under-estimated observa- statistics shown in Table 1 indicate a rather good agreement

tions. Lower correlation but improved modified bias was and a fair under-estimation of in-situ observed variables.

achieved in the central parts of NAS and in the Basin. Indicative comparative profiles of water temperature and

salinity for sites in Thracian Sea and Sporades Basin are shown

in Fig. 4.

Table 1 Spatially-mean statistical measures for ELCOM

model validation in terms of SST.

3.2. Model results description

Parameter 2006 2007 2008

The simulated surface flow exhibits similar patterns to those

Satellite-derived SST

produced by other recent NAS models (Androulidakis and

Correlation coefficient, r 0.917 0.924 0.941

Kourafalou, 2011; Androulidakis et al., 2012; Kopasakis

Mean squared-error, MSE 4.985 5.060 3.838

et al., 2012) and in-situ observations (Eronat and Sayin,

Nash-Sutcliffe effectiveness 0.774 0.779 0.818

2014; Sayin et al., 2011; Sylaios, 2011). In winter (09 February

coefficient, E

2008), the Dardanelles low salinity flow bifurcates around

Special correlation 0.993 0.993 0.995

Lemnos Island, with its northern branch crossing the Lemnos-

coefficient, Rs

Imvros Passage, moving eastwards towards Chalkidiki Penin-

Modified model bias, MMB 1.063 1.024 0.966

sula (Fig. 5). The flow around Athos Peninsula and into

Temperature Salinity

Singitikos Bay agrees to the Lagrangian observations of Olson

et al. (2007). Under Ekman transport, the southern Darda-

Year 2006 CTD casts

nelles branch flows around the southern coasts of Lemnos

Correlation coefficient, r 0.859 0.794

Island, turning westwards to feed a weak anticyclone in the

Mean squared-error, MSE 6.410 1.383

Sporades Basin. This pattern is consistent to the observations

Nash-Sutcliffe effectiveness 0.402 0.138

made by Olson et al. (2007) using drifters when reported on

coefficient, E

the enhanced westward Ekman drift associated with the

Special correlation 0.990 0.999

strong northerly winds. A strong anti-cyclonic flow with a

coefficient, Rs

large diameter (70 km) is formed in the vicinity of the BSW-

Modified model bias, MMB 0.921 0.975

LIW front, to the north-west of Lesvos Island.

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Modeling the buoyancy-driven Black Sea Water outflow into the North Aegean Sea 7

Figure 3 Spatial variability of (a) the correlation coefficient and (b) the modified model bias, between the modeled and the GHRSST

sea-surface temperature datasets.

In spring (08 May 2008) the wind influence lessens and as towards Thassos Island, it separates developing a twin cyclo-

3 1

BSW outflow remains at substantial levels (50,000 m s ), nic—anti-cyclonic system to the west and north-west of Samo-

1

its northwestern branch achieves speeds up to 1 [m s ], thraki Island. This twin cyclone—anticyclone system was also

strongly affecting the Thracian Sea (Fig. 6). This low salinity simulated by Androulidakis et al. (2012) during the summer

water (33.7—34.5) forms the Samothraki Anticyclone, a period (August 2003). The BSW-LIW frontal zone was found to

distinctive feature in Thracian Sea. Part of the BSW flow the south and east of Lemnos Island, allowing the south-

reaches the southwestern part of Thassos Island, and bifur- western water transfer towards Skiros Basin. Again, Androu-

cates into a branch moving towards Strymonikos Gulf and lidakis et al. (2012) points out the strong south-western pro-

another towards Athos Peninsula. Similar features were also pagation of surface waters and the presence of Sporades

produced by the model of Androulidakis et al. (2012). Anticyclone during the entire summer.

A circulation snapshot representing the summer conditions

of moderate south-eastern winds and diminished BSW outflow 3.3. PEA distribution and change

is shown in Fig. 7 (05 July 2008). BSW flow follows a westward

pathway between Lemnos and Imvros Islands, with speeds The PEA quantifies the deficit in the potential energy due

1

fl

ranging from 0.7 to 0.95 m s . As ow moves northwards to stratification over a water column of 200 m depth, as

Figure 4 Modeled and observed profiles (surface to 200 m depth) in the Thracian Sea (circle) for (a) water temperature and (b)

salinity and in the Sporades Basin (diamond) for (c) water temperature and (d) salinity, in summer 2006.

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8 N. Kokkos, G. Sylaios

Figure 7 Surface flow and salinity patterns in the North Aege-

Figure 5 Surface flow and salinity patterns in the North Aege-

an Sea as produced by ELCOM model on 05 July 2008.

an Sea as produced by ELCOM model on 09 February 2008.

compared to that of the fully mixed water column. The PEA column stratification reduces, and PEA values peak at

3 3

distribution in NAS increases due to the BSW buoyancy outflux 650 J m and 580 J m , respectively.

and the solar radiation effect and diminishes under the wind To understand the mechanisms responsible for the strati-

mixing influence. Fig. 8 presents the PEA temporal variability fication—mixing dynamics over NAS, the individual terms of

at selected sites in the Thracian Sea, in Lemnos Basin, to the Eq. (6) were explored and their relative contribution on

south of Lemnos Island and in Sporades Basin for year f-change was accounted for. In the Thracian Sea, during

3

2008. Results illustrate the PEA characteristic bell-shaped January 2008, mean water column density of 1028.11 kg m ,

5 4

curve resulting from the incident heat flux seasonality. In the mean density gradient of 1.41 10 kg m , mean wind

1 2

Thracian Sea and Lemnos Basin sites, the sudden PEA changes speed of 5.8 m s and mean solar radiation of 92 W m

are attributed to increased BSW bulges reaching the site were considered. The wind impact on f-change may be

6 3

(positive change) and to wind impact and the LIW originated estimated at 3.62 10 W m , the influence of solar radia-

5 3

masses entrapped through eddies at the site (negative tion is an order of magnitude higher (1.41 10 W m ),

change). For example, the significant PEA reduction pro- while the buoyancy flux effect induced by BSW contributes

3 3

duced in the Thracian Sea and Lemnos Basin between 26 June the most (1.23 10 W m ). During July 2008, solar heat

2

2008 and 04 July 2008 is attributed to the intrusion and flux reached 330 W m thus depth-averaged density

3

entrapment of saltier Levantine origin water, while wind reduced to 1026.80 kg m , while the depth-averaged den-

1 3 4

mixing (10 m s ) is responsible for a similar sudden change sity gradient decreased slightly at 1.18 10 kg m . As

on 12 October 2008. Moving to the south of Lemnos Island and wind speeds decreased, the wind effect on f-change reached

6 3

towards Sporades Basin, the impact of BSW on the water 2.1 10 W m , the influence of solar heat flux increased

5 3

approximately by a factor of four (7.4 10 W m ), while

the BSW impact almost halved compared to winter

4 3

(7.9 10 W m ), but remained the dominant stratifica-

tion mechanism.

Integrating the above results over a monthly period during

2006—2008, the relative contribution of each term on the

total PEA may be examined. Table 2 presents the mean

monthly f-values for Thracian Sea, as obtained from calcu-

lated vertical density distribution and the use of Eq. (5), and

the integrated monthly f-values as obtained through

Eq. (7). The results obtained by both methods appear rather

comparative. Moreover, the relative contribution of each

mechanism (solar radiation, buoyancy effect and wind

impact) on the mean-monthly PEA value is also shown. The

solar radiation contribution on the water column PEA depicts

3

an average value of 130.79 J m , ranging between

3 3

55.28 J m in January and 55.86 J m in December up to

3

208.02 J m in July. These findings appear in agreement

with the North Aegean sea-atmosphere heat fluxes analysis

Figure 6 Surface flow and salinity patterns in the North Ae- developed by Poulos et al. (1997) and Androulidakis et al.

gean Sea as produced by ELCOM model on 08 May 2008. (2012). In the same month, the BSW buoyancy contribution

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Modeling the buoyancy-driven Black Sea Water outflow into the North Aegean Sea 9

Figure 8 Temporal change of the potential energy anomaly at (a) the Thracian Sea (solid black line), (b) the Lemnos Basin (red

dashed line), (c) the south of Lemnos Island (blue dotted line) and (d) the Sporades Basin (green dashed-dotted line) during 2008. The

map shows the exact location of stations at the Thracian Sea (circle), the Lemnos Basin (triangle), the south of Lemnos Island (star) and

the Sporades Basin (diamond). (For interpretation of the references to color in this figure legend, the reader is referred to the web

version of this article.)

3

also receives its maximum value (611.98 J m ), leading to accounting for the effect of BSW buoyancy outflux crossing the

the most stratified water column having a f-stratification transect in the east-to-west direction (positive values), ranges

3 4 3 4 3

value of 811.27 J m . The wind impact reaches its maximum from 0.914 10 W m to +3.926 10 W m . Positive

3

f-contribution in January (22.19 J m ), producing a rather values prevail throughout the year, indicating that BSW is

well-mixed water column in the Thracian Sea, since the mostly transferred westward, towards the Thracian Sea

3

fTOTAL value is limited to 94.94 J m . (Fig. 9b). This westward transferred f-advective flux appears

related to the presence of Samothraki Anticyclone, an eddy

fi

3.4. Quanti cation of PEA equation terms system with 50—60 km diameter spread over the Thracian

Sea. The depth-mean straining term, explained as the

Fig. 9 presents the temporal variation in the magnitude of effect of tidal shear on the vertically constant horizontal

the examined potential energy equation terms crossing density gradients appears of lower magnitude than the

5 3

the Northern Lemnos—the Thracian Sea meridional transect f-advective term, ranging between 0.671 10 W m

5 3

during 2008 (A: 40.4758N, 25.2418E; B: 40.0228N, 25.2418E). and +0.440 10 W m (Fig. 9c). Similarly, limited is the

4 3

The df/dt term varies between 1.014 10 W m and variability of the non-mean straining (term C), while

4 3

+1.389 10 W m (Fig. 9a), while the f-advective term, the vertical mixing term (term E, Fig. 9e), expressed as

Table 2 The Thracian Sea mean monthly PEA, as computed by model results and monthly-integrated PEA and relative PEA-

contribution of individual terms as derived from Eq. (7) during 2006—2008.

3 3 3 3

Months Mean monthly fTOTAL [J m ] fSOLAR [J m ] fBOUYANCY [J m ] fWIND [J m ]

3

PEA [J m ]

January 103.83 94.94 55.28 62.27 22.19

February 104.04 115.97 70.55 54.89 9.17

March 224.71 206.22 120.10 95.87 9.57

April 308.49 317.18 156.73 163.05 2.57

May 613.32 601.80 206.76 398.15 3.08

June 786.51 673.00 200.03 475.02 2.02

July 755.01 811.27 208.02 611.98 8.70

August 774.92 761.55 195.60 567.40 1.42

September 662.56 633.02 141.20 497.36 5.51

October 431.28 455.27 96.64 368.29 9.64

November 249.55 292.79 62.79 235.60 5.56

December 163.08 172.46 55.86 121.66 5.03

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10 N. Kokkos, G. Sylaios

4 3 4 3

Figure 9 Temporal variability of (a) the df/dt-term (10 W m ), (b) the f-advective term (10 W m ), (c) the f-depth-mean

5 3 5 3 3 3

straining term (10 W m ), (d) the f-non-mean straining term (10 W m ), (e) the f-vertical mixing term (10 W m ) and (f)

3 3

the surface heating buoyancy introduction terms (10 W m ), crossing the north-west BSW branch. All terms were smoothed using a

low-pass-filter of 0.2 Hz cutoff frequency. Black lines in subplot (b) represent periods of Samothraki Anticyclone presence in Thracian

Sea.

the integrated vertical buoyancy flux, fluctuates between near is related to the strengthening of the SW branch, with

3 3 1

zero and 0.012 10 W m , obtaining increased negative increased flow up to 0.6 m s moving from the south-eastern

values under the influence of strong southern and north-east- cape of Lemnos towards Island. The Sporades

1

ern winds (15—20 m s ). The impact of solar heating, dom- anticyclone appears mostly supported by high positive

inating terms G & F, increases during the summer obtaining a f-advective values, as on 09 March 2008 when USW-

4 3 1 4 3

maximum value of 0.155 10 W m and reduces to near branch = 0.72 m s , the fadvective term 0.60 10 W m

zero values in the winter (Fig. 9f). and an anticyclonic flow is formed in Sporades (Fig. 11a).

The variability of the f-equation terms crossing an indica- Similar conditions prevail on 20 March 2008 (fadvective term

4 3

tive meridional transect for the BSW south-western branch (C: 0.83 10 W m ), as shown in Fig. 11b. Under a negative

39.5738N, 25.2418E; D: 39.1238N, 25.2418E), is shown in sign, the SW branch of BSW is weak or completely absent, and

Fig. 10. The positive sign in the f-advective term (Fig. 10b) the flow at the south of Lemnos Island is narrowed to the

4 3 4 3

Figure 10 Temporal variability of (a) the df/dt-term (10 W m ), (b) the f-advective term (10 W m ), (c) the f-depth-

5 3 5 3 3 3

mean straining term (10 W m ), (d) the f-non-mean straining term (10 W m ), (e) the f-vertical mixing term (10 W m )

3 3

and (f) the surface heating buoyancy introduction terms (10 W m ), crossing the south-west BSW branch. All terms were smoothed

using a low-pass-filter of 0.2 Hz cutoff frequency.

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Modeling the buoyancy-driven Black Sea Water outflow into the North Aegean Sea 11

Figure 11 Surface water circulation in North Aegean Sea (a) on 09 March 2008, when the fadvective term of SW-branch

4 3

0.60 10 W m , related to an anticyclone in Sporades Basin, (b) on 20 March 2008, when the fadvective term of SW-branch

4 3

0.83 10 W m , related to an anticyclone in the Sporades Basin, (c) on 28 May 2008, when the fadvective term of SW-branch

4 3

0.80 10 W m , related to a cyclonic flow in the Sporades Basin, and (d) on 2 June 2008, when the fadvective term of SW-branch

4 3

1.30 10 W m , related to a cyclonic flow in the Sporades Basin.

coastal zone, with a westward direction. Strong negative As seen from model results, the BSW bifurcation at the north

fadvective term values appear linked to the occurrence of a and south of Lemnos Island and the relative strength of flow

cyclonic flow in NE Sporades Basin, as on 28 May 2008 between these branches, determines the variability of the

4 3

(fadvective 0.80 10 W m ; Fig. 11c) and 02 June above described meso-scale patterns and the water column

4 3

2008 (fadvective 1.30 10 W m ; Fig. 11d). Sudden stratification-mixing processes, expressed by the potential

changes in the f-advective term sign occur mostly during energy anomaly of the studied system. The north-western

August and September (Fig. 10b), leading to consequent BSW flow affects mostly the circulation in the Thracian Sea,

changes on the vorticity sign of Sporades Basin flow. feeding sub-basin scale gyres and flows along the Thracian

coastline (the Coastal Current) and between Lemnos Basin

and Chalkidiki Peninsula (the Rim Current). The strong south-

4. Discussion western BSW flow enhances the horizontal density gradients

across the BSW-LIW frontal zone and affects the Skiros and

In this paper, ELCOM model rather successfully simulated the Sporades Basins inducing cyclonic—anti-cyclonic flows (the

variability of surface circulation and water masses distribu- Sporades Eddy). The above described results appear in agree-

tion in the North Aegean Sea, producing the rapidly changing ment to the circulation patterns described explicitly by Tzali

surface meso-scale patterns and the water column dynamics et al. (2010), Androulidakis and Kourafalou (2011) and

under the BSW, meteorological and heat exchange influence. Androulidakis et al. (2012).

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12 N. Kokkos, G. Sylaios

The potential energy anomaly variability illustrated the winds. Sylaios (2011) explained that under northerly winds,

importance of BSW outflux in the stratification conditions of the anticyclone was pushed towards the north-west of Lem-

the water column. Our results suggest that during the winter nos Island, while under the influence of south to south-

the impact of BSW-induced buoyancy on water column stra- westerly winds, it moved to the north-west of Samothraki

tification is higher by almost two orders of magnitude than Island. As shown by the temporal variation of the f—vertical

that of solar radiation. During spring and summer, solar heat mixing term (Fig. 9e), in the North Aegean Sea, strong winds

1

flux gradually increases, allowing BSW buoyancy impact as (>15 m s ) tend to destroy the anticyclonic pattern, pro-

the dominant f-change term, determining the water column moting vertical water column mixing. Indeed, the negative

stratification in the Thracian Sea, but only being an order of peaks in the temporal variability of term-E (20 February 08;

magnitude higher than the solar radiation effect. At the area 21 April 08; 30 May 08; 18 June 08; 11 July 08; 20 July 08;

of Sporades, solar radiation and buoyancy effects appear 14 September 08) correspond to short-to-medium scale

1

comparable during the summer period, while at Chios Basin storms with wind speeds between 15 and 20 m s .

f-temporal variability shows limited mean-monthly fluctua- Based on model results for the Thracian Sea, the baro-

tion and solar radiation dominates the water column clinic Rossby radius of deformation for Samothraki Antic-

dynamics. yclone was computed, as:

To comprehend the impact of BSW pulses advection on the

c1

¼ ;

North Aegean Sea, the general dynamic f-equation, as R1 (13)

jfj

derived by Burchard and Hofmeister (2008), was solved along

a meridional transect in the Thracian Sea, utilizing the where c1 is the gravity baroclinic wave speed, estimated by:

ELCOM model results for the upper 130 m. The f-advective Z

1 0

term crossing the NW branch appears mostly positive, imply- c1 ¼ NðzÞ dz; (14)

p

ing the westward transport of the buoyant jet. The term H

fluctuates strongly in time and receives its highest values

with N(z) the Brunt-Väisälä frequency. The produced R1

during spring and summer, related to the occurrence of a values during the occurrence of increased positive values

meso-scale eddy spread between Samothraki and Thassos in the cross-transect f-advective term exhibits a mean value

Islands. Based on the modeled flow field, the relative vorti-

of 7.5 0.3 km throughout 2008. This result is in agreement

city of this system, known as Samothraki Anticyclone, was

with the findings of Androulidakis and Kourafalou (2011),

calculated, as: during their numerical experimental tests. @v @u

z ¼ (12)

@x @y 5. Conclusions

and then associated to the f-advective term. Relative vor-

ticity in the Thracian Sea exhibits negative values (mean In this paper the three-dimensional model ELCOM was

5 1

z = 1.1 10 s ), indicating the anticyclonic nature of adapted, implemented and validated, aiming to derive

fi

the circulation. A fifth-order polynomial regression between the hydrodynamic eld in the North Aegean Sea. The Black

fl

relative vorticity and cross-transect f-advection is shown Sea Water out ow and spreading governs surface hydrody-

(Fig. 12), indicating that Samothraki Anticyclone was fed namics, with two distinct branches (NW and SW) at Lemnos

by the north-western branch of the BSW plume. A similar Island. Intensive post-processing on the validated model

analysis was also performed by Soosaar et al. (2014) on the results was carried out, aiming to link BSW buoyancy transfer

anticyclonic eddy of the southern Gulf of Riga and its rela- to NAS water column dynamics and surface meso-scale

tionship to the wind and horizontal density gradients. Results patterns.

fi

depicted that this anticyclone was mostly fed by the buoy- The potential energy anomaly illustrated a signi cant

ancy field, being enhanced or reversed by the dominant spatial variability in NAS, due to the variable impact of

BSW throughout the system's surface. PEA forcing analysis

indicated that BSW induces buoyancy comparable to the solar

heating impact on the winter water column stratification of

the Thracian Sea. However, in spring and summer, the BSW

influence in the Thracian Sea appears up to three times

higher than the corresponding solar heating effect. In Spor-

ades, solar radiation and buoyancy impact seem of equal

importance for summer water column stratification. Analysis

and quantification of the individual PEA terms exhibits the

impact of BSW-induced buoyancy on the surface meso-scale

patterns of NAS. Indeed, the f-advective term crossing the

NW branch exhibits strong relation to the occurrence of

Samothraki Anticyclone. A non-linear regression between

eddy's relative vorticity and the NW f-advective term was

developed, explaining the impact of BSW NW branch on

Samothraki Anticyclone.

Figure 12 Non-linear regression between the f-advective Similarly, a SW branch enhancement, indicated by the

term crossing the north-west BSW branch and the relative highly positive f-advective values, appears related to the

vorticity of Samothraki Anticyclone. intensification of Sporades Anticyclone. On the contrary,

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Modeling the buoyancy-driven Black Sea Water outflow into the North Aegean Sea 13

negative values in the f-advective term appear related to the Kontoyiannis, H., Kourafalou, V.H., Papadopoulos, V. , 2003. Seasonal

characteristics of the hydrology and circulation in the Northwest

occurrence of a cyclone in Sporades Basin. This vorticity sign

Aegean Sea (eastern Mediterranean): observations and modeling.

change occurred mostly during August and September 2008,

J. Geophys. Res. 108 (C9), 3302, http://dx.doi.org/10.1029/

associated to the sudden changes in the f-advection term

2001JC001132.

crossing the SW BSW branch. As shown by the variability of

1 Kopasakis, K.I., Georgoulas, A.N., Angelidis, P.B., Kostovinos, N.E.,

the f—vertical mixing term, strong winds (>15 m s ) tend to

2012. Numerical modeling of the long-term transport, dispersion,

destroy the above meso-scale eddy systems, thus promoting

and accumulation of Black Sea pollutants into the North Aegean

vertical water column mixing in NAS.

coastal waters. Estuar. Coast. 35 (6), 1530—1550, http://dx.doi.

org/10.1007/s12237-012-9540-9.

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